How to compute such resultant?

asked 2022-09-26 19:00:28 +0100

DreDd
39 ●1 ●6

updated 2022-10-02 21:03:44 +0100

5251 ●3 ●44 ●116

I need to compute such resultant: $https://latex.codecogs.com/svg.image?f(x) = {Res}_y ({A}_1 (y), {C}_0 (x) + y{C}_1 (x))$ Where $https://latex.codecogs.com/svg.image?{A}_1, {C}_0, {C}_1$ - polynomials over Z.

How can i do this in sage?

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answered 2022-09-26 19:54:40 +0100

rburing

10919 ●4 ●80 ●218 https://www.rburing.nl/

Setup:

R.<x> = PolynomialRing(ZZ)
A1 = R.random_element(degree=2)
C0 = R.random_element(degree=2)
C1 = R.random_element(degree=2)
S.<y> = PolynomialRing(R)

Execution:

sage: A1(y).resultant(C0 + y*C1)
x^4 - 6*x^3 + 5*x^2 - 4*x + 2

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Thanks, I tried to set a polynomials over another fields, especially C1, and face with data type problem, would it be correct to use change_ring to bring everything into the same form?

DreDd ( 2022-09-26 22:59:15 +0100 )edit

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Asked: 2022-09-26 19:00:28 +0100

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Last updated: Sep 26 '22

How to compute such resultant? edit